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How to challenge high attainers in maths

Sunday, 4 January 2015
Primary teachers continue to face the inherent difficulties of how to challenge high attainers in maths while making sure all the children in the class are making progress. Levels may be confined to history in many schools, but those children who are working at whatever is equivalent to Level 6 are still with us. 
I still get more requests for advice on teaching Level 6 than anything else, so it obviously still remains an issue. The new focus on Maths Mastery has muddied the water a little as well. Do we now worry a little less about differentiation and keep the class together before moving onwards and upwards? Possibly, but then shouldn’t we maintain high expectations and not put a ceiling on what the children can achieve? In reality this just increases that attainment gap because our high attainers just love to learn and so accelerate further away from the mere ‘average’ child (and out of sight of the strugglers).
So… what is the answer? I think that the first thing for teachers to be clear on are the connections between teaching and assessing, while recognising the differences between them. Assessment for Learning is inextricably linked to your teaching. It helps you identify what the children understand or are able to do to enable you to teach them the next step in their learning. You then use questions and activities to assess their learning and progress formatively, encouraging the children to self-assess.
However, we should not be thinking about teaching 'Level 6' maths - that is more about assessing children's attainment rather than teaching. We should be planning for appropriate modeled or supported activities and active learning experiences that aims just beyond what the child can already comfortably achieve. If this happens to be at Level 6 or Y6A* or whatever label is used to show a very high attaining child, then this is fine. Formative and summative assessments can be used to verify their attainment and progress.

Another key thing to be clear on is whether you are teaching content beyond the primary curriculum or using problem-solving and reasoning to add scope for higher order thinking, possibly from a simple starting point.
KS3 content is pretty accessible to many Y6 children and, in fact, the new 2014 Programmes of Study for Y6 includes a lot of the old KS3 curriculum – circle properties, pie chart construction, mappings, equations… and more. So, if you have a unit focusing on shape for example, I see no problem in looking at the KS3 content to find some aspects that will be a useful step on for your high attainers. For instance, congruent and similar shapes may be something new you could teach.
My main efforts, however, would be to look at opportunities for problem-solving and reasoning to challenge all your class, including your high-attainers. Nrich call them ‘low threshold high ceiling tasks’ and it is an apt description. Activities that are accessible to the majority of your class but have the potential to develop and provide challenge are perfect for giving all children the chance to make progress. They are often simple starting points using practical resources or an image to support the opening problem. It is then the teacher’s role to prompt and question so that the children use reasoning or problem-solving strategies to follow a line of enquiry. 

These tasks, most importantly, allow a focus on the process skills rather than knowledge – predicting, convincing, generalising, being systematic, questioning, investigating… all part of two of the aims of the 2014 NC – reasoning and problem-solving.

So… how can you plan so that the high attainers are appropriately challenged?

1. Start with your maths focus
Identify the objectives and the expected outcomes to work out the appropriate level for groups in your class.
2. Gather problem-solving activities and investigations
Spend a little time trawling through your books, resources and favourite websites (like Nrich) for ideas that may be useful as ‘low ceiling high threshold’ tasks.
3. Choose your theme
This won't be used for every maths lesson, but it will draw together some of the lessons, putting the maths in context to give opportunities to challenge.
4. Adapt the problems to fit the theme.
There may be one or two large problems to solve over a period of time or smaller problems to solve on different days.

Most importantly, give the children time to absorb themselves in the maths and the desire to explore and investigate. They need to experience getting stuck and making mistakes so that they also feel the ‘Aha!’ moments when they make a discovery, see a pattern or find an answer. These are the children that will go on to enjoy and succeed in their maths, rather than ‘force-feeding’ them content that may seem a little purposeless if it is merely picked out as ‘Level 6’ maths.
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